Whereas the possibilities for classifying are multiple given the huge number of properties chemical elements have, an exceptional example stressing ordering over similarity for the case of the table is the definition from Wikipedia: ‘The periodic table is a tabular arrangement of the chemical elements, ordered by their atomic number, electron configurations, and recurring chemical properties’. The suitability of partitions for periodic systems is discussed later.ĭespite the relevance of similarity and order for the periodic system, 2 they are considered as separate aspects of it, with some emphasis on classification 3 caused by the, taken for granted, ordering of the elements based upon atomic number. a collection of subsets not sharing elements. As similarity is used for classifying, it is worth mentioning that a customary outcome of a classification is a partition (definition A.3), i.e. In contrast to order, similarity, represented as ∼, is only reflexive and symmetric, that is, self-similarity is allowed (Na∼Na) and if Na is similar to K (Na∼K), then K∼Na (definition A.2). If E is the set of elements, its order by ≺ _ is denoted as ( E, ≺ _). In short, an order relation is reflexive, antisymmetric and transitive (definition A.1). In addition, if H ≺ _He, and He ≺ _Li, then H ≺ _Li. It holds that if He ≺ _ x and if x ≺ _He, then x is He. An order relation holds that every element is related to itself, e.g. Let us take H, He and Li and their atomic numbers, which we order with the usual order on natural numbers, denoted by ≺ _. After considering that current tables interchange Mendeleev's columns and rows and that the ‘arranging’ criteria have been replaced by the atomic number, two important relations are the salient structure keepers of the table, and in general of the periodic system: order and similarity.īefore going any further, let us analyse these two relations through examples. In his 1869 publication, Mendeleev wrote: ‘if one arranges the elements in vertical columns according to increasing atomic weight, such that the horizontal rows contain analogous elements, also arranged according to increasing atomic weight, one obtains the following table’ (p. 221 of ).’ In this paper, we report a formal structure for periodic system, based on a contemporary mathematical interpretation of 1869 Mendeleev publication and recent studies of the system. Īs noted by Mendeleev: 1 ‘the reason for the absence of any explanation concerning the nature of the periodic law resides entirely in the fact that not a single rigorous, abstract expression of the law has been discovered (p. Instead, they give insights on the possible chemical and physical causes of the patterns depicted by the system but have failed in providing a formal structure for it. However, almost 150 years after its announcement, the different approaches from quantum chemistry, group theory, clustering and information theory, to name but a few, have not led to a unified picture. Since the formulation of the periodic system in the 1860s, the quest for understanding its structure has intensively motivated research in different areas of chemistry and physics.
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